A148298 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 0, 0), (-1, 1, 1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 5, 13, 36, 112, 350, 1155, 3925, 13579, 48220, 173836, 635911, 2360420, 8850743, 33549545, 128312974, 494688957, 1921574844, 7512968389, 29555315723, 116910451943, 464810687871, 1856740321151, 7448936153798, 30004699108624, 121312614191899, 492189426529433, 2003421447498019

Offset

0,3

Links

Table of n, a(n) for n=0..29.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A271272 A148296 A148297 * A148299 A148300 A038982

Adjacent sequences: A148295 A148296 A148297 * A148299 A148300 A148301

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved